WASHINGTON — Thirty years after failing to convince the Supreme Court of the threat posed by home video recordings, big media companies are back and now trying to rein in another technological innovation they say threatens their financial well-being.

The battle has moved out of viewers’ living rooms, where Americans once marveled at their ability to pop a cassette into a recorder and capture their favorite programs or the sporting event they wouldn’t be home to see.

Now the entertainment conglomerates that own U.S. television networks are waging a legal fight, culminating in Tuesday’s Supreme Court argument against a startup business that uses Internet-based technology to give subscribers the ability to watch programs anywhere they can take portable devices.

The source of the companies’ worry is Aereo Inc., which takes free television signals from the airwaves and sends them over the Internet to paying subscribers in 11 cities. Aereo, backed by billionaire Barry Diller, has plans to more than double that total.

Broadcasters including ABC, CBS, Fox, NBC and PBS have sued Aereo for copyright infringement, saying Aereo should pay for redistributing the programming the same way cable and satellite systems do.

The U.S. networks increasingly are reliant on these retransmission fees, estimated at $3.3 billion last year and going up to more than $7 billion by 2018, according to research by SNL Kagan, which analyzes media and communications trends. They fear that they will lose some of that money if the Supreme Court rules for Aereo.

Aereo’s service starts at $8 a month and is available in New York, Boston, Houston and Atlanta, among others. Subscribers get about two dozen local over-the-air stations, plus the Bloomberg TV financial channel.

In the New York market, Aereo has a data center in Brooklyn with thousands of dime-size antennas. When a subscriber wants to watch a show live or record it, the company temporarily assigns him an antenna and transmits the program over the Internet to the subscriber’s laptop, tablet, smartphone or other device.

The antenna is only used by one subscriber at a time, and Aereo says that’s much like the situation at home, where a viewer uses a personal antenna to watch over-the-air broadcasts for free.

“Aereo is in some ways novel, but it is also among a host of technologies that uses the Internet to offer consumers the ability to do what they always have more cheaply and conveniently,” the Dish Network and Echostar Technologies said in a supporting legal brief filed in the Supreme Court.

But the broadcasters and their backers argue that Aereo’s competitive advantage lies not in its product, but in avoiding paying for it.

“Aereo is simply a blatant free rider trying to make a quick buck without paying anything toward the true costs of what it misappropriates,” Time Warner Inc. said in a court filing.

The broadcasters told the court that Aereo’s “competitors pay for the rights to retransmit ‘live TV’ to the public — as they must to avoid liability for copyright infringement — while Aereo does not.”

The federal appeals court in New York ruled that Aereo did not violate the copyrights of broadcasters with its service, but a similar service has been blocked by judges in Los Angeles and Washington, D.C.

The 2nd U.S. Circuit Court of Appeals said its ruling stemmed from a 2008 decision in which it held that Cablevision Systems Corp. could offer a remote digital video recording service without paying additional licensing fees to broadcasters because each playback transmission was made to a single subscriber using a single unique copy produced by that subscriber. The Supreme Court declined to hear the appeal from movie studios, TV networks and cable TV channels.

In the Aereo case, a dissenting judge said his court’s decision would eviscerate copyright law.

Judge Denny Chin called Aereo’s setup a sham and said the individual antennas are a “Rube Goldberg-like contrivance” — an overly complicated device that accomplishes a simple task in a confusing way — that exists for the sole purpose of evading copyright law.

The Obama administration, artists, actors, Major League Baseball and the National Football League all support the broadcasters. But the administration and computer software and telecommunications groups are urging the court to avoid a broad ruling in favor of copyright protection that could call into question the rapidly evolving world of cloud computing, which gives users access to a vast online computer network that stores and processes information.

FM radio and cable TV were initially derided as unnecessary, inefficient or just bizarre, said the digital civil liberties watchdog Electronic Frontier Foundation. In a legal filing joined by other public interest groups and the consumer electronics trade association, the group said the justices should not become regulators of technology and “the court should not attempt to predict the future of television.”

The entertainment industry has changed dramatically since the high court ruled in favor of home video recording in 1984 in a 5-4 decision. Then, Sony was the maker of the Betamax recorder and Universal City Studios and Walt Disney Productions were arguing for protection under copyright law.